L^p-estimates of the Boltzmann equation around a traveling local Maxwellian

In this paper, we are interested in the Lp-estimates of the Boltzmann equation in the case that the distribution function stays around a traveling local Maxwellian. For this, we divide both sides of the Boltzmann equation by the velocity distribution function with a fractional exponent and reformulate the Boltzmann equation into a regularized one. This amounts to endowing additional integrability on the collision kernel, which in turn enables us to apply simple Hölder type inequalities. Our results cover the whole range of Lebesgue exponents: 0<p≤∞.